Thread: The FTA in an Odd Degree Polynomial

This is my problem:

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1. How can the Fundamental Theorem of Algebra be used to show that any polynomial of
odd degree has at least one root?

Make sure that:

1. every claim is justified

2. a classmate reading your answer would understand

3. vocabulary is used correctly

4. the solution is vivid (there are no missing details)

5. your answer is concise (verbose answers are virtually impossible to understand)


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I'm thinking this forum is more suitable for the question because I'm more likely to get a simpler response. Thanks in advance, will +rep anyone who significantly helps.

That's very strangely stated! The "fundamental theorem of algebra" states directly that every polynomial has at least one root, not just those of odd degree. Is it possible that the statement should be "every polynomial, having all real coefficients, of odd degree, has at least one real root"?

It's only Algebra 1050, and the teacher wants us just to grasp the concept. He's not looking for anything ground-breaking. I see your point, but could you please give me an answer in layman's terms? :P

Okay, first, what is the "fundamental theorem of algebra"?